It seems to me that with ever larger and better telescopes and powerful statistical methods, humans are gleaning surprising amounts of information from observations of distant stars. I am especially impressed that we are able to not only to detect the presence of, but also look at the spectrum of, extrasolar planets.

Are there information-theoretic limits to what observational astronomy can discover (per second)? I expect there must be, because each star only sends a finite number of photons to Earth (per second), and surely each photon conveys a finite amount of information.

Is this a well-defined question, and if so, what are they---has there been any work exploring these limits?